Measuring Shape with Topology

@article{Macpherson2010MeasuringSW,
  title={Measuring Shape with Topology},
  author={R. D. Macpherson and Benjamin Schweinhart},
  journal={ArXiv},
  year={2010},
  volume={abs/1011.2258}
}
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We demonstrate the utility and computability of this measure by applying it to branched polymers, Brownian trees, and self-avoiding random walks. 

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